Theme Essential Question: How do we use equations to model real world situations?
Essential Questions: How can you give examples of equations with a given number of solutions?
Standards Analyze and solve linear equations. 8.EE.7.A Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
Objectives The student will use their skill in solve linear equation in one variable to investigate and analyze the three possible outcome:
One solution
No solutions
Infinite solutions
Reflections and/or Comments from your PCSSD 8th Grade Curriculum Team We had previously suggested that this lesson be introduced and/or consolidated with solving equations with variables on both sides.
This lesson has strong implications for Mathematical Practice #3. Students can make supportive arguments based on prior knowledge, (make conjectures, provide counterexamples, build a logical argument), for the three possible solutions to a linear equation (one solution, no solution, infinite solution). Time has been provided to allow students to have this level of interaction.
When do you know an equation has infinite number of solutions?
When do you know an equation has no solution?
Observable Student Behaviors
Students are able to deal with all possible solutions when solving linear equations.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Vocabulary variables, expressions, equations, like terms, distributive property, conjecture
Suggested Activities
Houghton Mifflin OnCore Mathematics Middle School Grade 8 Unit 3-2
ABC Mastering the Common Core in Mathematics Chapter 4 Lesson 6, P. 41-42
Gizmo Lessons
Solving Equations with Decimals
Solve an equation involving decimals using dynamic arrows on a number line.
Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps.
Teaching the Common Core Math Standards with Hands-On Activities by Judith Muschla (page 176-177)
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
This video introduces students to the basics of solving simple equations while practicing how to change word problems into number sentences or equations. The concept of solving equations is demonstrated using a balance scale. Always remember that the two sides of the equation must remain equal for the scale to stay balanced.
Discovery Education: Math Masery: Equations
This video includes the following chapters:* Unknowns, Reciprocals, and Signed Numbers * Absolute Value and Solving Equations * Multiplying Equations and Working with Unknowns * Working with Unknowns * Solving Word Problems with Equations * Solving Equations in Two Steps * Solving Word Problems with Equations * Working with Unknowns * Solving Two-Step Equations and Word Problems * Working with Unknowns in the Denominator * Working with Exponents * Working with Roots and Exponents (Teacher Guide Available)
Discovery Education: Solving Equations: Part 01
This video lays out the basic rules and tactics of solving for unknown variables in simple algebraic equations. Explaining important concepts like identities, inverses, and balancing the equation, this video establishes a firm ground for tackling the multiple-step problems introduced in Part Two.
Discovery Education: Solving Equations: Part 02
This video helps us solve multiple-step algebraic equations by applying the numeric operations learned in Part One and provides helpful strategies and handy shortcuts for approaching problems with fractions, negative signs, and variables with coefficients. Lastly, the video explains strategies for working with literal equations, problems containing more than one unknown variable.
http://webmath.com/solver.htmlThis page will show you how to solve an equation for some unknown variable. Note: Please do not type and "=" signs. It is already put in for you. You just need to type in the expressions on the left and right side of the "=" sign.
Content: Analyzing Solutions
Theme Essential Question: How do we use equations to model real world situations?
Essential Questions:
How can you give examples of equations with a given number of solutions?
Standards
Analyze and solve linear equations.
8.EE.7.A Solve linear equations in one variable.
Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
Objectives
The student will use their skill in solve linear equation in one variable to investigate and analyze the three possible outcome:
Reflections and/or Comments from your PCSSD 8th Grade Curriculum Team
We had previously suggested that this lesson be introduced and/or consolidated with solving equations with variables on both sides.
This lesson has strong implications for Mathematical Practice #3. Students can make supportive arguments based on prior knowledge, (make conjectures, provide counterexamples, build a logical argument), for the three possible solutions to a linear equation (one solution, no solution, infinite solution). Time has been provided to allow students to have this level of interaction.
Background Information
Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials.
http://www.azed.gov/wp-content/uploads/PDF/MathGr8.pdf
Assessment
It is recommended that students be assessed, at the end of this unit, on their ability to solving equations.
Product
Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary
variables, expressions, equations, like terms, distributive property, conjecture
Suggested Activities
- Houghton Mifflin OnCore Mathematics Middle School Grade 8 Unit 3-2
- ABC Mastering the Common Core in Mathematics Chapter 4 Lesson 6, P. 41-42
- Gizmo Lessons
- Solving Equations with Decimals
- Solve an equation involving decimals using dynamic arrows on a number line.
- Solving Two-Step Equations
- Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps.
- Teaching the Common Core Math Standards with Hands-On Activities by Judith Muschla (page 176-177)
Highly RecommendedDiverse Learners
Homework
Suggested:
Terminology for Teachers
What constitutes a viable argument?
Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination
High Yield Strategies
Similarities/Differences | Summarizing/Notetaking | Reinforcing/Recognition | Homework/Practice |
Non-Linguistic representation | Cooperative Learning | Objectives/Feedback |
Generating-Testing Hypothesis | Cues, Questions, Organizers
Resources
Professional Texts
Literary Texts
Informational Texts
- See New York Common Core Aligned Task (other resources)
http://schools.nyc.gov/Academics/CommonCoreLibrary/SeeStudentWork/default.htmArt, Music, and Media
Manipulatives
Games
Videos
SMART Board Lessons, Promethean Lessons
Websites
Other Activities, etc.
Language
Arts
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Matrix
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Home K-2
Home 3-6
Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6